Ummm Forerunner tech such as their cryptums and even their armor allows them to live for thousands of years, possibly unbelievably longer. But that just prevents death by age haha however, that does not change my belief that the Didact IS still alive and will be back for more.
Some argue that that speech was given after the firing of the rings during the Forerunner era, and he's explaining why they should keep humans as reclaimers, and that his reasoning is a prelude to future events in the series. Though I agree that either way, that dude is still out there. He fell through a slipspace rupture. He just landed somewhere else and went "damn it, gotta try again"
I thought that at first, but then he makes references to the fact that humanity has seized the Forerunners' triumphs as their own while they squandered eons in the darkness. It sounds like he's referring to the modern(well, futuristic) humans rather than the primitive cavemen of his time.
So I just rebeat it and listened. It still seems like it's a speech he gave after the rings were fired the first time, and he's urging the Forerunners to eradicate humanity rather than give them the Mantle.